What does "persuade you otherwise" mean exactly? Is it an idiom?
I don't think so, but it sounds like something that might have sexual undertones. "May I persuade you otherwise" means roughly, "May I convince you to change your mind about this?" It's less wordy than the idiomatic 'change your mind', and it sounds more eloquent.
persuade you otherwise - to give an alternate option over something that is already discussed,
e.g Mr. X wants to buy a property in this region but the Realtor wishes to persuade him otherwise.